Ind. Eng. Chem. Process Des. Dev., Vol. 18, No.
2, 1979
333
Modeling of Shallow Fluidized Bed Combustion of Coal Particles L. T. Fan,* K. Tojo, and C. C. Chang Department of Chemical Engineering, Kansas State University, Manhattan, Kansas 66506
The dynamic and steady-state characteristics of a shallow fluidized bed coal combustor have been studied by using a model in which the lateral solids mixing is taken into account. It has been found that the steady-state and unsteady-state concentrations in the bed are influenced profoundly by the bubble size, and that the effects of excess air rate, bed height, and particle density on the dynamic characteristics of the shallow fluidized bed coal combustor are negligible compared with the effect of bubble size.
Introduction I t is well known that one of the important advantages of a fluidized bed is that mixing of fluidized particles in it is intensive. This advantage is particularly appreciable in a small fluidized bed. However, in a large shallow fluidized bed, which is used to reduce blowing cost, lateral solid mixing can be poor, leading to appreciable nonuniformity in lateral concentration profiles. This nonuniformity may impair an effectual property of the shallow fluidized bed; that is, the bubble size remains small, thus giving rise to a high transfer rate of gas between the bubble and emulsion phases. The present work is concerned with dynamic and steady-state characteristics of a shallow fluidized bed coal combustor which has so far received relatively little attention. A dynamic model in which the lateral solids mixing is taken into account is developed. The effects of some operating variables on the solids concentration profiles are analyzed by means of the model in order to determine an effective method for promoting lateral solids mixing. Highley and Merrick (1971) studied the effect of solid feed points on the lateral solids mixing in a large fluidized bed reactor. Merry and Davidson (1973) have proposed a method of “Gulf Circulation” which is generated by introducing uneven distribution of fluidizing gas in order to promote the lateral solids mixing in a shallow fluidized bed. However, none of these works is specifically concerned with the shallow fluidized bed coal combustor. Mathematical Formulation The present model assumes that the reactor consists of two phases, namely, the bubble and emulsion phases. The assumptions of the model are as follows. (a) The voidage of the emulsion phase remains constant and is equal to that at the incipient state of fluidization. Thus the flow of gas through the bed in excess of minimum fluidization flow passes through the bed in the form of bubbles (see, e.g., Davidson and Harrison, 1963). (b) The emulsion phase is well mixed in the axial direction. This is a valid assumption for a relatively shallow fluidized bed. (c) The bubble size remains constant, and the flow of bubbles is of the plug flow. This assumption is valid since there is usually no sufficient time for the bubble to grow in a shallow fluidized bed. (d) The overall rate of combustion reaction represented as
c+0 2
- coz
is so high that the oxygen transfer into coal particles is the rate-determining step (see, e.g., Avedesian and Davidson, 1973). (e) No elutriation occurs. (f) The bed is under isothermal operation. These assumptions give rise to the following governing equations (see Appendix)
bubble phase: aCab - K(Cab - Cae) aX
aCab ~
at emulsion phase: aCae
urn,
at
L
emf - = -(Cao
(1)
+r
Cae)
-
K(Cab -
k, cae)d X - 6 CC,,
(2)
pd,
for oxygen, and
aC _ at
for carbon particles. The appropriate initial and boundary .. . conditions-are: for t = 0 Cab = Cae = CaO for t > 0 Cab = CaOat x = 0 (bed bottom) aC/ar = aCab/ar = aCae/ar = 0 at r = 0 (center of the bed) aC/ar = aCab/ar = aCae/ar = 0 at r = R (wall of the bed) The feeding rate function, +,, is defined by
F
at 0 Ir 5 rf arf2(1 - tb)L =O atrf
